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Edexcel IGCSE Maths (4MA1) · Unit 4: Graphs & Functions

IGCSE Maths Trigonometric Graphs Questions and Answers

Trigonometric Graphs questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 2 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.

Practise trigonometric graphs in Unit 4 →Graphs, Sequences and Calculus revision notes

What this topic covers

Trigonometric Graphs worked examples

Worked example 1: Solving with the sine graph

Solve \(\sin x=0.5\) for \(0^\circ\le x\le360^\circ\).

Solution

  1. \(\sin^{-1}0.5=30^\circ\).
  2. The sine graph is symmetrical about \(90^\circ\), so the other solution is \(180-30=150^\circ\).

Answer: \(30^\circ,\ 150^\circ\)

Tip: Sketch the graph to see how many solutions there are.

Worked example 2: Solving tan x = k

Solve \(\tan x=-1.5\) for \(0^\circ\le x\le360^\circ\).

Solution

  1. \(\tan^{-1}(-1.5)=-56.3^\circ\), outside the range.
  2. tan has period \(180^\circ\): add 180 and 360.
  3. \(x=123.7^\circ\) or \(303.7^\circ\).

Answer: \(123.7^\circ,\ 303.7^\circ\)

Tip: Solutions of tan x = k are always 180° apart.

Trigonometric Graphs exam-style questions

Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.

Question 1 · easy · 1 mark

Write down the period of the graph of \(y=\tan x\).

Show the answer and mark scheme
  • B1 180°

Answer: 180°

Question 2 · medium · 3 marks

Solve \(\tan x=2\) for \(0^\circ\le x\le360^\circ\). Give your answers to 1 decimal place.

Show the answer and mark scheme
  • M1 tan⁻¹ 2
  • A1 63.4°
  • B1 243.4° ft their first angle + 180

Answer: \(x=63.4^\circ,\ 243.4^\circ\)

Question 3 · hard · 2 marks

How many solutions does the equation \(\tan x=5\) have for \(-360^\circ\le x\le360^\circ\)? Give a reason.

Show the answer and mark scheme
  • M1 one solution found (78.7°) and period 180° used
  • A1 4

Answer: 4

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise trigonometric graphs for the exam

Questions students ask

Which Edexcel IGCSE Maths papers test trigonometric graphs?

Either Higher tier paper, 1H or 2H, can test trigonometric graphs: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more trigonometric graphs questions?

In the IGCSE student hub: Unit 4 (Graphs & Functions) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

More Unit 4 topics: Graphs & Functions